{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T06:11:55Z","timestamp":1769926315948,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T00:00:00Z","timestamp":1683849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Anhui University Natural Sciences fund","award":["Kj2019A073"],"award-info":[{"award-number":["Kj2019A073"]}]},{"name":"Anhui University Natural Sciences fund","award":["HAB202231"],"award-info":[{"award-number":["HAB202231"]}]},{"name":"Natural Science Foundation of Huaian","award":["Kj2019A073"],"award-info":[{"award-number":["Kj2019A073"]}]},{"name":"Natural Science Foundation of Huaian","award":["HAB202231"],"award-info":[{"award-number":["HAB202231"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we discuss the existence of a positive periodic solution for a first-order nonlinear neutral differential equation with impulses on time scales. Based on the Leggett\u2013Williams fixed-point theorem and Krasnoselskii\u2019s fixed-point theorem, some sufficient conditions are established for the existence of positive periodic solution. An example is given to show the feasibility and application of the obtained results. Since periodic solutions are solutions with symmetry characteristics, the existence conditions for periodic solutions also imply symmetry.<\/jats:p>","DOI":"10.3390\/sym15051072","type":"journal-article","created":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T09:26:13Z","timestamp":1683883573000},"page":"1072","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Positive Periodic Solutions for a First-Order Nonlinear Neutral Differential Equation with Impulses on Time Scales"],"prefix":"10.3390","volume":"15","author":[{"given":"Shihong","family":"Zhu","sequence":"first","affiliation":[{"name":"College of Mathematics and Computer, Tongling University, Tongling 244601, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4484-8789","authenticated-orcid":false,"given":"Bo","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1451","DOI":"10.1016\/j.mcm.2010.06.009","article-title":"Three positive periodic solutions to nonlinear neutral functional differential equations with impulses and parameters on time scales","volume":"52","author":"Wang","year":"2010","journal-title":"Math. 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